Rafail Abramov
Department of Mathematics, Statistics and Computer Science
University of Illinois at Chicago
851 S. Morgan St.
Chicago, IL 60607
E-mail: abramov@math.uic.edu
Phone: (312) 413 7945
Publications
R. Abramov, Improved linear response for stochastically
driven systems, submitted to Journal of Nonlinear Science
on January 13, 2010.
[PDF] [arXiv.org]
R. Abramov, Linear response for slow variables of
deterministic or stochastic dynamics with time scale
separation, submitted to Journal of Computational Physics
on August 18 2009.
[PDF]
(preprint)
Update Jan 8 2010: the first round review
process is still ongoing, and I have not been asked yet to
make a revision. However, I completed additional numerical
simulations with stronger fast-slow coupling, which I plan to
submit in the revision. Here is the updated version of the
manuscript: [PDF]. Simulations
with weak coupling are excluded from this update.
A. Majda, R. Abramov & B. Gershgorin, High skill in
low frequency climate response through fluctuation dissipation
theorems despite structural instability, Proceedings of
the National Academy of Sciences, 2009.
[PDF
at PNAS website]
R. Abramov, Short-time linear response with reduced-rank
tangent map, Chinese Annals of Mathematics, 2009.
[PDF] (preprint)
R. Abramov, The multidimensional maximum entropy moment
problem: A review on numerical methods, Communications in
Mathematical Sciences, 2009, vol. 8, no. 2,
377—392.
[PDF]
(preprint)
R. Abramov, The multidimensional moment-constrained
maximum entropy problem: A BFGS algorithm with constraint
scaling, Journal of Computational Physics, 2009,
vol. 228, 96—108.
[DOI
link]
R. Abramov & A. Majda, A new algorithm for low
frequency climate response, Journal of the
Atmospheric Sciences, 2009, vol. 66, 286—309.
[DOI link]
R. Abramov & A. Majda, New approximations and tests of
linear fluctuation-response for chaotic nonlinear
forced-dissipative dynamical systems, Journal of
Nonlinear Science, 2008, vol. 18, 303—341.
[PDF]
R. Abramov & A. Majda, Blended response algorithms for
linear fluctuation-dissipation for complex nonlinear dynamical
systems, Nonlinearity, 2007, vol. 20, 2793—2821.
[PDF]
R. Abramov, An improved algorithm for the multidimensional
moment-constrained maximum entropy problem, Journal of
Computational Physics, 2007, vol. 226, 621—644.
[DOI
link]
R. Abramov, A practical computational framework for the
multidimensional moment-constrained maximum entropy
principle, Journal of Computational Physics, 2006,
vol. 211, 198—209.
[DOI
link]
A. Majda, R. Abramov & M. Grote, Information theory
and stochastics for multiscale nonlinear systems, vol. 25
of CRM Monograph Series, Centre de Recherches
Mathématiques, Université de
Montréal. Published by American Mathematical Society,
2005. ISBN 0-8218-3843-1. 141 pp.
[Amazon]
[Barnes
& Noble]
K. Haven, A. Majda & R. Abramov, Quantifying
predictability through information theory: Small sample
estimation in a non-Gaussian framework, Journal of
Computational Physics, 2005, vol. 206, 334—362.
[DOI
link]
R. Abramov, A. Majda & R. Kleeman, Information Theory
and Predictability for Low Frequency Variability, Journal
of Atmospheric Sciences, 2005, vol. 62, no. 1,
65—87.
[PDF]
R. Abramov & A. Majda, Quantifying uncertainty for
non-Gaussian ensembles in complex systems, SIAM Journal
on Scientific Computing, 2003, vol. 26, no. 2,
411—447.
[PDF]
R. Abramov & A. Majda, Discrete approximations with
additional conserved quantities: Deterministic and statistical
behavior, Methods and Applications of Analysis, 2003,
vol. 10, no. 2, 151—190.
[PDF]
R. Abramov & A. Majda, Statistically relevant
conserved quantities for truncated quasi-geostrophic
flow, Proceedings of the National Academy of Sciences, 2003,
vol. 100, no. 7, 3841—3846.
[PDF]
R. Abramov, G. Kovačič & A. Majda, Hamiltonian
structure and statistically relevant conserved quantities for
the truncated Burgers-Hopf equation, Communications in
Pure and Applied Mathematics, 2003, vol. 56,
1—46.
[PDF]
Ph.D. Rensselaer Polytechnic
Institute, Department of
Mathematics, 2002.
Thesis title: Statistically
relevant and irrelevant conserved quantities for the
equilibrium statistical description of the truncated
Burgers-Hopf equation and the equations for barotropic
flow.
[PDF]
Software
The multidimensional moment-constrained maximum entropy algorithm
This page is currently under heavy construction, however the full algorithm library for the i586 platform is there with few examples in C, C++ and FORTRAN (see file maxent_dist.tar.gz). The proper manual is currently lacking.
Teaching
MATH 210 — Calculus III